Question

To supplement your​ retirement, you estimate that you need to accumulate

​$360,000 exactly 38 years from today. You plan to make​ equal, end-of-year deposits into an account paying  11 % annual interest.

a.  How large must the annual deposits be to create the

​$360, 000 fund by the end of 38 ​years?

b.  If you can afford to deposit only ​$590 per year into the​account, how much will you have accumulated in 38 years?

Answer 1

a) $765.13 b) $277,601.23

Explanation:

a) The problem is an example of an ordinary annuity (deposits at the end of the period).

The future value of this type of annuity is:

`FV=A*((1+i)^(n) -1)/(i)`

Clearing the annual deposit A

`A=FV*(i)/((1+i)^(n) -1)`

`A=360,000*(0.11)/((1.11)^(38)-1 ) =360,000*0,002125351=765.13`

The deposit needed to have $360,000 in 38 years is $765.13

b) We can use the same formula to compute the FV of a known deposit:

`FV=A*((1+i)^(n) -1)/(i)`

`FV=590*((1.11)^(38) -1)/(0.11)=590*470,5105644=277,601.23`

With annual deposits of $590 you will have at 38 years an ammount of $277,601.23